Trumps helicopter isn't based at PIK.
Yes it is:
As part of the partnership, the exact details of which remain unclear, Trump and Prestwick will be offering transfers to Trump Turnberry via the Trump corporation’s private helicopter.
Read more at: Donald Trump announces Prestwick link up - The Scotsman
You all seem to forget that once he is President he will not be allowed to fly in any of his private aircraft - only official US Air Force craft.
Do you have a source for that? As president, he can do what he wants (well, within reason). It's been done before, they even have a call-sign for civilian aircraft carrying the president - Executive One.